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Many computational tasks can be naturally expressed as a composition of a DNN followed by a program written in a traditional programming language or an API call to an LLM. We call such composites "neural programs" and focus on the problem of learning the DNN parameters when the training data consist of end-to-end input-output labels for the composite. When the program is written in a differentiable logic programming language, techniques from neurosymbolic learning are applicable, but in general, the learning for neural programs requires estimating the gradients of black-box components. We present an algorithm for learning neural programs, called ISED, that only relies on input-output samples of black-box components. For evaluation, we introduce new benchmarks that involve calls to modern LLMs such as GPT-4 and also consider benchmarks from the neurosymbolic learning literature. Our evaluation shows that for the latter benchmarks, ISED has comparable performance to state-of-the-art neurosymbolic frameworks. For the former, we use adaptations of prior work on gradient approximations of black-box components as a baseline, and show that ISED achieves comparable accuracy but in a more data- and sample-efficient manner. 

Foundation models have vast potential to enable diverse AI applications. The powerful yet incomplete nature of these models has spurred a wide range of mechanisms to augment them with capabilities such as in-context learning, information retrieval, and code interpreting. We propose Vieira, a declarative framework that unifies these mechanisms in a general solution for programming with foundation models. Vieira follows a probabilistic relational paradigm and treats foundation models as stateless functions with relational inputs and outputs. It supports neuro-symbolic applications by enabling the seamless combination of such models with logic programs, as well as complex, multi-modal applications by streamlining the composition of diverse sub-models. We implement Vieira by extending the Scallop compiler with a foreign interface that supports foundation models as plugins. We implement plugins for 12 foundation models including GPT, CLIP, and SAM. We evaluate Vieira on 9 challenging tasks that span language, vision, and structured and vector databases. Our evaluation shows that programs in Vieira are concise, can incorporate modern foundation models, and have comparable or better accuracy than competitive baselines. 

We study the problem of synthesizing a core fragment of relational queries called select-project-join (SPJ) queries from input-output examples. Search-based synthesis techniques are suited to synthesizing projections and joins by navigating the network of relational tables but require additional supervision for synthesizing comparison predicates. On the other hand, decision tree learning techniques are suited to synthesizing comparison predicates when the input database can be summarized as a single labelled relational table. In this paper, we adapt and interleave methods from the domains of relational query synthesis and decision tree learning, and present an end-to-end framework for synthesizing relational queries with categorical and numerical comparison predicates. Our technique guarantees the completeness of the synthesis procedure and strongly encourages minimality of the synthesized program. We present Libra, an implementation of this technique and evaluate it on a benchmark suite of 1,475 instances of queries over 159 databases with multiple tables. Libra solves 1,361 of these instances in an average of 59 seconds per instance. It outperforms state-of-the-art program synthesis tools Scythe and PatSQL in terms of both the running time and the quality of the synthesized programs. 

Synthesizing relational queries from data is challenging in the presence of recursion and invented predicates. We propose a fully automated approach to synthesize such queries. Our approach comprises of two steps: it first synthesizes a non-recursive query consistent with the given data, and then identifies recursion schemes in it and thereby generalizes to arbitrary data. This generalization is achieved by an iterative predicate unification procedure which exploits the notion of data provenance to accelerate convergence. In each iteration of the procedure, a constraint solver proposes a candidate query, and a query evaluator checks if the proposed program is consistent with the given data. The data provenance for a failed query allows us to construct additional constraints for the constraint solver and refine the search. We have implemented our approach in a tool named Mobius. On a suite of 21 challenging recursive query synthesis tasks, Mobius outperforms three state-of-the-art baselines Gensynth, ILASP, and Popper, both in terms of runtime and accuracy. We also demonstrate that the synthesized queries generalize well to unseen data. 

Motivated by distributed data processing applications, we introduce a class of labeled directed acyclic graphs constructed using sequential and parallel composition operations, and study automata and logics over them. We show that deterministic and non-deterministic acceptors over such graphs have the same expressive power, which can be equivalently characterized by Monadic Second-Order logic and the graded µ-calculus. We establish closure under composition operations and decision procedures for membership, emptiness, and inclusion. A key feature of our graphs, called synchronized series-parallel graphs (SSPG), is that parallel composition introduces a synchronization edge from the newly introduced source vertex to the sink. The transfer of information enabled by such edges is crucial to the determinization construction, which would not be possible for the traditional definition of series-parallel graphs. SSPGs allow both ordered ranked parallelism and unordered unranked parallelism. The latter feature means that in the corresponding automata, the transition function needs to account for an arbitrary number of predecessors by counting each type of state only up to a specified constant, thus leading to a notion of counting complexity that is distinct from the classical notion of state complexity. The determinization construction translates a nondeterministic automaton with n states and k counting complexity to a deterministic automaton with 2 n 2 states and kn counting complexity, and both these bounds are shown to be tight. Furthermore, for nondeterministic automata a bound of 2 on counting complexity suffices without loss of expressiveness. 

While serverless platforms substantially simplify the provisioning, configuration, and management of cloud applications, implementing correct services on top of these platforms can present significant challenges to programmers. For example, serverless infrastructures introduce a host of failure modes that are not present in traditional deployments. Individual serverless instances can fail while others continue to make progress, correct but slow instances can be killed by the cloud provider as part of resource management, and providers will often respond to such failures by re-executing requests. For functions with side-effects, these scenarios can create behaviors that are not observable in serverful deployments. In this paper, we propose mu2sls, a framework for implementing microservice applications on serverless using standard Python code with two extra primitives: transactions and asynchronous calls. Our framework orchestrates user-written services to address several challenges, such as failures and re-executions, and provides formal guarantees that the generated serverless implementations are correct. To that end, we present a novel service specification abstraction and formalization of serverless implementations that facilitate reasoning about the correctness of a given application’s serverless implementation. This formalization forms the basis of the mu2sls prototype, which we then use to develop a few real-world microservice applications and show that the performance of the generated serverless implementations achieves significant scalability (3-5× the throughput of a sequential implementation) while providing correctness guarantees in the context of faults, re-execution, and concurrency.